Higher inductive types (HITs) in Homotopy Type Theory allow the definition of datatypes
which have constructors for equalities over the defined type. HITs generalise quotient types …

Formal constructive type theory has proved to be an effective language for mechanized
proof. By avoiding non-constructive principles, such as the law of the excluded middle, type …

Homotopy theory can be developed synthetically in homotopy type theory, using types to
describe spaces, the identity type to describe paths in a space, and iterated identity types to …

Bidirectional transformations (BX) serve to maintain consistency between different
representations of related and often overlapping information, translating changes in one …

Dependent type theories are a family of logical systems that serve as expressive functional
programming languages and as the basis of many proof assistants. In the past decade, type …

Colimits are a fundamental construction in category theory. They provide a way to construct
new objects by gluing together existing objects that are related in some way. We introduce a …

As software becomes increasingly complex, software configuration management is
becoming ever more important. This paper shows how logics for reasoning about mutable …

A structural diffing algorithm compares two pieces of tree-shaped data and computes their
difference. Existing structural diffing algorithms either produce concise patches or ensure …

We look at computational physics from an electrical engineering perspective and suggest
that several concepts of mathematics, not so well-established in computational physics …

The Unix diff utility that compares lines of text is used pervasively by version control systems.
Yet certain changes to a program may be difficult to describe accurately in terms of …